Write an equation of the line passing through the point (-10,3) that is parallel to the line 5x+2y=12. (in y=mx+b form)

Two lines are parallel if they never meet, and we can say that two lines will be parallel if and only if they have the same slope and different y-intercept.

We will find that the solution here is y = -2.5*x + 28

Let's see how to get that solution:

First, we can write our line as a general line, like:

y = a*x + b

Where a is the slope and b is the y-intercept.

Now we want this line to be parallel to:

5x + 2y = 12

First, let's rewrite the above line in slope-intercept form, to do that, we need to isolate y in one side of the equation.

2y = 12 - 5x

y = 12/2 -(5/2)*x

y = 6 - 2.5*x

Now we know the slope of this line, and remember, the parallel line will have this same slope, then our line will be:

y = -2.5*x + b

To find the value of b, we can use the fact that this line passes through the point (-10, 3). This means that when x = -10, we have y = 3

Replacing these in the line equation we get:

3 = -2.5*10 + b

3 = -25 + b

3 + 25 = b

28 = b

Then the equation of the line is:

y = -2.5*x + 28

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The answer to your question is:        y = -5/2 x - 22

Step-by-step explanation:

Data

A ( -10, 3)

Parallel to 5x + 2y = 12

Process find slope (m)

                                        5x + 2y = 12

                                        2y = -5x + 12

                                        y = (-5/2) x + 12/2

                                        y = (-5/2) x + 6

slope = m = -5/2

                            (y - y1) = m(x - x1)

                            ( y - 3) = -5/2 ( x + 10)

                            y - 3 = -5/2 x - 50/2

                            y = -5/2 x - 25 + 3

                            y = -5/2 x - 22

c

step-by-step explanation:

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